Convexity, complexity, and high dimensions
Stanislaw J. Szarek
Case Western Reserve University, Cleveland, United States
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Abstract
We discuss metric, algorithmic and geometric issues related to broadly understood complexity of high dimensional convex sets. The specific topics we bring up include metric entropy and its duality, derandomization of constructions of normed spaces or of convex bodies, and different fundamental questions related to geometric diversity of such bodies, as measured by various isomorphic (as opposed to isometric) invariants.